This creates a rift valley.
The best example is the one between the Arabian plate and the African plate. These two are separating and the result is the Red Sea. The African Rift Valley is actually the African plate splitting in two. The parts of East Africa and Horn of Africa will eventually be separated from the main African plate and form their own plate that will separate. This will cause the African rift valley to turn into a sea like the Red Sea, eventually.
If this happens mid ocean, the result is a mid-ocean ridge.
This is actually rare. The only place this is really happening is on the West Coast of North America. Here, there is slippage and subduction along the length of California. The result is a fracture zone where the Coast mountain ranges of California are beign pulled apart from the Sierra Nevada mountains and the Central Valley is forming in between them.
Eventually, the Central Valley will sink into an ocean, and the Coast range of California will be torn off into a new island...and new plate. The most notable thing about this area is the San Andreas Fault, one of the largest and potentially destructive faults in the world. There are, of course, other places with bad earthquakes, many of which are also around the Pacific Rim. Those earthquakes are caused by...
This is the specific situation you are asking about. Where either two plates are moving into each other or one plate is crashing into another plate that is not moving in the other direction, you have subduction. Here you have one plate submerge under another, driving up high volcanic mountains. Examples are the Cascades and Aleutian chain in British Columbia and Alaska, and the Andes in South America.
In particular, this happens with an oceanic plate meeting a continental plate. If it is two continental plates you get...
Continental collisions also cause maintain building; but the results are less volcanic. This is the process behind the Alps and mountains of the Balkans and Anatolia where the European and African plates are meeting. It is also famously the factor behind the Himalayas.